d. dealing with the uncertainty- I am keen to try an Empirical
Bayes approach to accounting for these different sources of
uncertainty. Some of you might be familiar with Adrian Raftery's
(http://www.stat.washington.edu/raftery/Research/Whales/whales.html)
(and others) work with the Int'l Whaling Commission for modeling
Bowhead whale pop dynamics. He uses a Bayes Empirical Bayes
approach that the Int'l Whaling Commission now accepts as the
"std" methodology. There's some similarity with salmon
harvest mgmt problems and what I'm thinking about trying.
The Empirical Bayes approach is not really Bayesian per se,
it just recognizes that the parameters are random, like the
natural mortality rates in the ocean will vary from year to
year. We would formulate probability distributions for the
parameters- the probability distributions would have
"hyperparameters". E.g., the distribution of initial survival
rates is Beta with parameters alpha and beta. Then use the
historical data, e.g., 10 years of Grays Harbor coho, to estimate
the hyperparameters. Next to make a forecast for the coming
year could sample from the probability dist'ns for the parameters
and run the model. Could repeatedly do this to get a probability
distribution for the outputs- draw histograms of predicted escapement
for a stock, etc.
* what's the prognosis on getting historical coho data for effort
and CWT recoveries into rectangular matrices?
2. Non-normal state-space models.
- the normality assumption can lead to some unreasonable predicted
abundances and catches, negative ones, when abundance and effort
are quite low
- it might be better to use something like a Poisson dist'n for
the catches, (like Ray Hilborn did in a 1990 CJFAS article on tuna
migration) and maybe abundances
- this will require different techniques for estimating the historical
parameters (Monte Carlo methods), but the simulation for pre-season
planning might be simple
3. Integrating multiple types of fisheries.
- to deal with overlapping fisheries, say sport and troll, the catch
equations can be modified, and the observation equ'n in the SSM
modeled (haven't worked this out but don't think it'll be hard)
- to deal with fisheries for which the effort has different temporal
resolution will be trickier (e.g. monthly sport effort vs weekly
troll effort)
4. Other modifications to SSM
- more complex spatial framework for inside fisheries
- chinook maturation schedule/component
- links with or integration of ocean conditions
- putting in switch for catch ceiling/quotas
- selective fisheries
- incidental mortality
- *other things?
5. Going into "production mode"
- calculating historical parameter estimates for a wide range of
stocks over several years
- carrying out tests to determine what parameters are or are not
stock specific